Electric Power Systems Research 121 (2015) 89–100
Contents lists available at ScienceDirect
Electric Power Systems Research
journal homepage: www.elsevier.com/locate/epsr
Review
A review of power distribution planning in the modern power
systems era: Models, methods and future research
Pavlos S. Georgilakis ∗ , Nikos D. Hatziargyriou
School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), GR 15780 Athens, Greece
a r t i c l e
i n f o
Article history:
Received 12 March 2014
Received in revised form 9 October 2014
Accepted 7 December 2014
Keywords:
Power distribution planning
Power system planning
Distribution networks
Distributed energy resources
Optimization
Bibliography review
a b s t r a c t
In recent years, significant research efforts have been devoted to the optimal design of modern power
distribution systems. The aim of power distribution planning (PDP) is to design the distribution system
such as to timely meet the demand growth in the most economical, reliable, and safe manner possible. The
gradual transformation of the distribution grid from passive to active imposes the need to also consider
the effect of distributed generation and active demand during planning and the increased advantages of
their control. Several models and methods have been proposed recently for the solution of the modern
PDP problem. This paper presents an overview of the state of the art models and methods applied to the
modern PDP problem, analyzing and classifying current and future research trends in this field.
© 2014 Elsevier B.V. All rights reserved.
Contents
1.
2.
3.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PDP models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.
General problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.
Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.
Design variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.
Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.
Problem type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.
Planning period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.
Load models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.
Distributed generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.
Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10.
Taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PDP methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.
Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.
Mixed integer linear programming (MILP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2.
Nonlinear programming (NLP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3.
Dynamic programming (DP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4.
Ordinal optimization (OO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.5.
Direct solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.
Heuristic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1.
Genetic algorithm (GA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2.
Tabu search (TS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
∗ Corresponding author. Tel.: +30 210 772 4378; fax: +30 210 772 3659.
E-mail addresses: pgeorg@power.ece.ntua.gr (P.S. Georgilakis), nh@power.ece.ntua.gr (N.D. Hatziargyriou).
http://dx.doi.org/10.1016/j.epsr.2014.12.010
0378-7796/© 2014 Elsevier B.V. All rights reserved.
90
90
90
90
91
91
91
91
91
91
91
91
91
91
91
91
91
94
94
94
94
94
90
4.
5.
6.
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
3.2.3.
Particle swarm optimization (PSO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4.
Evolutionary algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5.
Ant colony system (ACS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.6.
Bacterial foraging (BF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.7.
Simulated annealing (SA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.8.
Artificial immune system (AIS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.9.
Artificial bee colony (ABC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.10.
Practical heuristic algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.
Evaluation of PDP methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1.
Evaluation of numerical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2.
Evaluation of heuristic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Contribution of the reviewed works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.
Evolution of PDP requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.
Evolution of PDP methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
The designer of the power distribution system, in the context
of power distribution planning (PDP), has as a primary goal to
design the distribution system such as to timely meet the demand
growth in the most economical, reliable, and safe way. This is
not straightforward, because of the very large extension of the
power distribution system, as well as the fact that this system is
responsible for most of the electrical energy losses and most of the
interruptions due to faults. In general, the traditional PDP consists
of finding the most economical solution (single objective function)
with the optimal location and size (capacity) of future substations
and/or feeders to meet the future demand. The objective of the
traditional PDP is the minimization of an economic cost function
(the investment cost to add, reinforce or replace substations and/or
feeders, plus the energy loss cost), subject to a set of technical and
operational constraints.
In the last years the distribution planning function is further
complicated by the high penetration of distributed generation (DG)
technologies, including storage, and the participation of the consumers in the form of active demand, encouraged by national and
regional policies worldwide. This is the basic notion of the active
distribution network (ADN) that incorporates DG, distributed storage, active demand, automation, communication, and advanced
metering in its operational planning. It is now widely recognized
that by exploiting the capacity and control capabilities of the distributed energy resources (DER) at distribution level instead of
just connecting them to the network (the so-called “fit and forget”
approach) can provide optimal planning solutions with significant
cost savings. For example, the optimal placement of DG into existing
power distribution systems has already attracted the interest of significant research efforts [1] in the last twenty years, with the first
work published in 1994. An exhaustive review of PDP works has
been provided in [2–4], published in 1997, 2000, and 2002, respectively. As will be shown later in Table 2, with respect to modern
PDP of active distribution networks, the consideration of automatic
switching actions appears in 2005; consideration of DER integration and control appears in 2007; and consideration of multiple
controls (active and reactive power control of DG units, on-line
network reconfiguration, demand side response, and generation
curtailment) appears in 2008. This paper provides an overview of
selected PDP works published after 2005 (when the first modern
PDP appears) [5–81]. It should be noted that in [1], 83 state of the
art publications on the optimal placement of DG into existing power
distribution systems were reviewed, while in this paper, 77 completely different state of the art publications on modern PDP are
94
94
94
94
94
94
94
94
94
94
95
95
95
95
98
98
99
99
reviewed. More specifically, this paper reviews 77 selected PDP
articles, published after 2004, which optimize at least the feeders
and/or the substations of the distribution network. As will be shown
in this paper, the modern PDP models and methods are more integrated (e.g., simultaneously optimize the substations and feeders),
more often multiobjective, more often consider the installation of
DG simultaneously to the expansion of substations and feeders, and
more often consider DG control, load control and automatic switching actions, in comparison to the traditional PDP models of the past
[2–4].
This paper introduces a taxonomy of the state of the art PDP
models and methods, offering a unifying description of a relatively
large number of works devoted to the subject [5–81]. Moreover, this
work analyzes and classifies current and future research trends in
PDP. This review aims to serve as a guide to power system engineers
and researchers on the available PDP models and methods in the
modern power systems era.
The paper is organized as follows. Section 2 focuses on PDP
models, defines the general problem statement, outlines and classifies the published models and presents the objectives, constraints,
design variables, types of application, problem types, categories of
planning period, characteristics of load models, and types of distributed generation studied in PDP. Section 3 outlines and classifies
the published PDP methods. Section 4 discusses the contribution of
the reviewed works. Section 5 suggests future research ideas and
Section 6 concludes.
2. PDP models
2.1. General problem statement
The typical PDP consists of finding the most economical solution with the optimal location and size of future substations and/or
feeders to meet the future demand. The objective of the typical PDP
is the minimization of an economic cost function (e.g., the investment cost to add, reinforce or replace substations and/or feeders,
plus the energy loss cost), subject to a set of technical and operational constraints. The PDP is a complex mixed integer nonlinear
optimization problem.
2.2. Objective
This section is focused on the main objective
PDP problem. The PDP can be formulated as a
problem or a multiobjective problem. The main
functions minimize the net present value of the
functions of the
single-objective
single-objective
following costs:
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
(1) investment cost (to add, reinforce or replace substations and
feeders), plus energy loss cost; (2) investment and power loss cost;
(3) investment, loss, and reliability cost; (4) total costs (fixed and
variable): investment, loss, reliability, and operation and maintenance cost; or (5) total costs minus total revenues.
PDP multiobjective formulations can be classified as:
(1) multiobjective with weights, where the multiple objectives
are in fact transformed into a single objective thanks to the
user-defined fixed weights of the individual objectives; this
formulation belongs to the methods with a priori articulation
of preferences, which means that the user determines the relative importance of the objective functions before executing the
optimization algorithm [82];
(2) multiobjective, which belongs to the methods with a posteriori articulation of preferences, which means that an algorithm is
used to determine the Pareto optimal set (potential solutions),
and then, the decision-maker imposes preferences directly on
the Pareto optimal set, i.e., the decision-maker chooses a solution from the Pareto set [82].
2.3. Design variables
The following design variables (unknowns) are mainly computed: (1) feeders location (routing); (2) feeders location and size;
(3) substations location and size, feeders location; (4) substations
location and feeders location and size; (5) substations size and
feeders location and size; (6) substations and feeders location and
size; (7) substations location, feeders size, and load allocation (e.g.,
assignment of single-phase loads to the different phases, or load
balancing among phases); (8) substations location and size, feeders
size, and load allocation; (9) size of substations, distributed generation (DG) and feeders; (10) size of substations and DG, location
and size of feeders; and (11) substations, DG, and feeders location
and size.
91
2.7. Load models
The load profile is modelled in PDP as: (1) one load level; (2)
multi-load level; (3) probabilistic; or (4) fuzzy.
The loads are modelled as: (1) balanced three-phase; (2) unbalanced three-phase; or (3) a mix of single-phase and three-phase
loads.
In the active distribution networks, the loads are distinguished
as critical or inflexible (non-elastic) and as controllable or flexible
(elastic).
2.8. Distributed generation
The DGs can be owned: (1) by the utility, or (2) by private
investors and they can be: (1) thermal (dispatchable), or (2) renewable (mostly non-dispatchable) DGs.
2.9. Constraints
The most common constraints in the PDP formulation are: (1)
power flow equality constraints, (2) bus voltage or voltage drop
limits, (3) substation and feeder capacity limits, (4) use of standard
sizes for transformers and conductors, (5) radial operation of the
network, and (6) full connectivity, i.e., the network must supply all
buses. Moreover, the following constraints have been considered
in some PDP models: (7) budget constraint, (8) layout of cables in
urban areas according to the street map, (9) bus angle limits, (10)
transformer taps limits, (11) tapering conductor constraints, i.e.,
the upstream conductors must have a cross-section greater than
or equal to the downstream ones. In case of DG connection, the
following constraints have been considered: (12) capacity limits of
DGs, (13) total DG capacity penetration limit, (14) capacity reserve,
(15) short-circuit current limit.
2.10. Taxonomy
2.4. Distribution
The PDP is applied to: (1) the primary (medium voltage – MV)
distribution network, (2) the secondary (low voltage – LV) distribution network, and (3) the primary and the secondary distribution
network.
Table 1 presents a unifying taxonomy of the reviewed PDP models.
3. PDP methods
3.1. Numerical methods
2.5. Problem type
The optimization problem type can be: (1) design of new network that is based on the design of the whole network assuming
there is no real existing network; (2) network expansion that is
based on the optimal expansion of the existing network to serve
the future growth of current and new forecasted loads and DER;
or (3) application of PDP both for the design of new network and
network expansion.
2.6. Planning period
According to the model, the optimization problem can be: (1)
static that is also called single-stage, which determines the PDP
requirements in only one stage (planning period); or (2) dynamic
that is also called multistage, which determines the PDP requirements in successive expansion plans over several planning periods
(stages), thus representing the natural course of progression. More
useful results are offered by the dynamic approach, which is, however, more challenging because of the interdependency between
stages.
3.1.1. Mixed integer linear programming (MILP)
A multistage distribution expansion problem is formulated as
a MILP problem that is solved by a branch-and-bound algorithm
and/or standard commercial solvers [20,21,24,46]. An integral planning methodology of primary–secondary distribution systems is
formulated and solved using MILP [6]. A spatial PDP is formulated
and solved using MILP [52].
3.1.2. Nonlinear programming (NLP)
Continuous constrained NLP is applied for the solution of a
generalized horizon planning (20+ years ahead) model with ten
decision (design) variables [16,18]. A mixed-integer NLP (MINLP)
based PDP is solved by Benders decomposition [31]. A dynamic PDP
is formulated using two interrelated models, which are solved by
MILP and NLP, respectively [34].
3.1.3. Dynamic programming (DP)
DP solves a multistage PDP [19,40] and a multiobjective PDP
[65].
92
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
Table 1
Taxonomy of the reviewed power distribution planning models.
Reference
Distribution
Type
Period
Decisions (design variables)
Objective function
[5]
Secondary
Expansion
Static
[6]
Prim. + Second.
Expansion
Static
[7]
Secondary
Expansion
Static
[8]
Primary
Expansion
Static
Substations location, feeders
size, load allocation
Substations and feeders
location & size
Substations and feeders
location & size
Feeders location & size
[9]
Primary
Expansion
Static
[10]
Primary
Expansion
Static
[11]
Primary
Expansion
Static
Min total costs
(fixed + variable)
Min investment and energy
loss cost
Min investment and energy
loss cost
Min cost
(investment + loss + reliability)
Min investment and energy
loss cost
Min cost
(investment + loss + reliability)
Fuzzy multiobjective
[12]
Primary
New + Expan.
Static
[13]
Primary
Expansion
Static
[14]
Primary
Expansion
Static
[15]
Primary
Expansion
Dynamic
[16]
Prim. + Second.
Expansion
Static
[17]
Primary
Expansion
Static
[18]
Prim. + Second.
Expansion
Static
[19]
Primary
Expansion
Dynamic
[20]
Primary
Expansion
Dynamic
[21]
Primary
Expansion
Dynamic
[22]
Primary
New
Static
Substations and feeders size,
primary voltage
Substations, DGs, and feeders
location & size
Substations and DGs size,
feeders location & size
Substations and DGs size,
feeders location & size
Feeders location
[23]
Primary
Expansion
Dynamic
Feeders location & size
[24]
Primary
New
Dynamic
[25]
Primary
Expansion
Static
[26]
[27]
[28]
Primary
Primary
Primary
New
Expansion
Expansion
Static
Static
Static
[29]
Secondary
New
Static
[30]
Secondary
New
Static
[31]
Primary
Expansion
Static
[32]
Primary
Expansion
Dynamic
[33]
Secondary
New + Expan.
Static
[34]
Primary
Expansion
Dynamic
[35]
Primary
Expansion
Static
[36]
Primary
New
Static
[37]
Primary
New
Static
Substations location and size,
feeders location
Substations, DGs, and feeders
location & size
Feeders location & size
DGs and feeders location & size
Substations location and size,
feeders location
Substations and feeders
location & size
Substations and feeders
location & size
Substations and DGs size,
feeders location & size
Substations and feeders
location & size
Substations location & size,
feeders size, load allocation
Substations, DGs, and feeders
location & size
DGs location & size, feeders
location
Substations size, feeders
location & size
Feeders location & size
[38]
Primary
Expansion
Static
[39]
Primary
Expansion
Static
[40]
Primary
Expansion
Dynamic
[41]
Prim. + Second.
New + Expan.
Static
[42]
Primary
Expansion
Static
Substations location, feeders
location & size
Substations size, feeders
location & size
Substations and feeders
location & size
Substations and feeders
location & size
Substations and feeders
location & size
Substations and feeders
location & size
Substations, DGs, and feeders
size
Substations and feeders size,
primary voltage
Feeders location & size
Substations, DGs, and feeders
location & size
Substations and feeders
location & size
Feeders location & size
Substations and feeders
location & size
Feeders location & size
Multiobjective
Multiobjective
Min investment and energy
loss cost
Min total costs minus total
revenues
Min cost
(investment + loss + reliability)
Min total costs
(fixed + variable)
Min cost
(investment + loss + reliability)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min cost
(investment + loss + reliability)
Min investment and energy
loss cost
Multiobjective with weights
Min total costs
(fixed + variable)
Multiobjective
Multiobjective
Min investment and energy
loss cost
Min investment and energy
loss cost
Min investment and energy
loss cost
Min cost
(investment + loss + reliability)
Multiobjective with weights
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Multiobjective with weights
Min investment and power
loss cost
Multiobjective
Min total costs
(fixed + variable)
Min cost
(investment + loss + reliability)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
93
Table 1 (Continued)
Reference
Distribution
Type
Period
Decisions (design variables)
Objective function
[43]
Primary
New
Dynamic
Feeders location
[44]
Primary
New
Static
Feeders location & size
[45]
Secondary
New
Static
[46]
Primary
Expansion
Dynamic
[47]
Primary
Expansion
Dynamic
[48]
Prim. + Second.
New
Static
[49]
Primary
Expansion
Static
[50]
Primary
New
Static
Substations and feeders
location & size
Substations and feeders
location & size
Substations, DGs, and feeders
location & size
Substations and feeders
location & size
DGs and feeders location &
size, switches status
Feeders location
[51]
Primary
New
Static
[52]
[53]
Primary
Primary
Expansion
New
Static
Static
[54]
Primary
Expansion
Static
Min total costs
(fixed + variable)
Min investment and energy
loss cost
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min cost
(investment + loss + reliability)
Min investment cost
Min investment cost or max
DG penetration
Multiobjective
[55]
Primary
Expansion
Dynamic
[56]
Primary
New
Static
[57]
Primary
Expansion
Dynamic
[58]
Primary
New
Static
[59]
Primary
Expansion
Static
[60]
Prim. + Second.
Expansion
Dynamic
[61]
Prim. + Second.
New + Expan.
Static
[62]
Primary
New
Static
Substations, DGs, and feeders
location & size
Substations, DGs, and feeders
location & size
Substations and feeders
location & size
Feeders location & size
[63]
Primary
New + Expan.
Static
Feeders location & size
[64]
Primary
Expansion
Static
[65]
[66]
Primary
Primary
New + Expan.
Expansion
Static
Dynamic
[67]
Primary
Expansion
Dynamic
[68]
Primary
Expansion
Dynamic
[69]
Primary
Expansion
Dynamic
[70]
Secondary
New + Expan.
Static
[71]
Primary
Expansion
Dynamic
[72]
Primary
Expansion
Dynamic
[73]
[74]
Primary
Primary
Expansion
Expansion
Dynamic
Dynamic
[75]
Primary
Expansion
Static
DGs location or size, feeders
location
Feeders location & size
Substations, DGs, and feeders
location & size
Substations, DGs, and feeders
location & size
Substations, DGs, and feeders
location & size
Substations, DGs, and feeders
location & size
Substations and feeders
location & size
Substations, DGs, and feeders
location & size
Substations, DGs, and feeders
location & size
DGs and feeders location & size
Substations and feeders
location & size
Feeders location & size
[76]
Primary
Expansion
Static
Feeders location
[77]
Primary
Expansion
Dynamic
[78]
Primary
Expansion
Static
[79]
Primary
New
Static
DGs, feeders, and smart
metering location & size
Substations, feeders, and charg.
stat. location & size
Feeders location & size
[80]
Primary
New
Static
[81]
Primary
Expansion
Static
Substations and feeders
location
Feeders location
Feeders location
Substations and feeders
location & size
Substations, DGs, and feeders
location & size
Substations and feeders
location
Substations, DGs, and feeders
location & size
Feeders location & size
Feeders location & size,
reclosers location
Substations, feeders, and charg.
stat. location & size
Min total costs
(fixed + variable)
Min investment and energy
loss cost
Min total costs
(fixed + variable)
Min investment and energy
loss cost
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min cost
(investment + loss + reliability)
Min cost
(investment + loss + reliability)
Multiobjective with weights
Multiobjective with weights
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Max a return-per-risk index
Max a return-per-risk index
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Multiobjective
Multiobjective
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Min total costs
(fixed + variable)
Multiobjective
Min total costs
(fixed + variable)
Multiobjective with weights
Min total costs
(fixed + variable)
94
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
3.1.4. Ordinal optimization (OO)
OO simultaneously optimizes PDP and electric vehicle charging
stations planning [81].
3.2.5. Ant colony system (ACS)
A dynamic ACS algorithm solves a PDP that considers the
installation of DG together with the reinforcement of feeders and
substations [15].
3.1.5. Direct solution
The optimal feeder routing is solved by a direct approach that
depends only on tracking radial paths and computing the cost of
the paths [51,56].
3.2.6. Bacterial foraging (BF)
A BF technique solves the optimal feeder routing problem [50].
3.2. Heuristic methods
3.2.7. Simulated annealing (SA)
The PDP is solved by SA in combination with a steepest descent
method [22] and in conjunction with MILP in [75].
3.2.1. Genetic algorithm (GA)
GA is applied for the solution of PDP problem
[7,32,37,49,60,61,64,70]. The PDP is solved by GA in combination with quasi-Newton [9], optimal power flow (OPF) [47,57],
and branch exchange [62]. A balanced GA in combination with data
envelopment analysis solves multistage PDP under uncertainty
[43]. GA is combined with graph theory to solve a PDP considering
DG connection [35]. GA is applied to solve two problems: (1) the
optimal MV substation problem, and (2) the optimal HV substations placement and feeders routing problem [28]. An interior
point method embedded discrete GA co-optimizes DG and smart
metering allocation simultaneously with network reinforcement
[77]. A multiobjective GA is combined with geographic information
systems to solve the PDP of open-loop MV networks [26]. A nondominated sorting GA (NSGA) is applied for PDP [13,73]. NSGA-II,
a variant of NSGA, is used to solve a multiobjective PDP [12,38]. A
GA with problem-specific fix, crossover and mutation operators
solves a multistage PDP [23]. A recombination-based evolutionary
approach is used for finding the optimal distribution network
topology [8]. The planning of secondary distribution networks is
formulated as a MINLP problem that is solved by an evolutionary
approach [5]. A strength Pareto evolutionary algorithm (SPEA) is
applied for PDP [13,27].
3.2.2. Tabu search (TS)
A fuzzy model for the multiobjective PDP problem is solved by a
TS method that computes the nondominated solutions corresponding to the simultaneous minimization of the fuzzy economic cost,
the fuzzy expected nonsupplied energy, and the risk of overloading the feeders and/or substations [11]. The LV PDP of a real size
distribution company is effectively solved by the method of [33]
in combination with Voronoi diagrams and TS [30]. A constructive
heuristic algorithm (CHA) in conjunction with TS solves the LV PDP
[33]. A PDP considering DG and uncertainties is solved by TS with an
embedded Monte Carlo simulation based probabilistic power flow
model [79]. Multiobjective TS solves a dynamic PDP [74]. Multiobjective reactive TS in combination with CHA and GA solve a PDP
[54]. TS and simulated annealing (SA) have been applied to solve
the PDP and the conclusion is that TS is more efficient than SA [36].
3.2.3. Particle swarm optimization (PSO)
The MV and LV networks are simultaneously designed by a
discrete PSO (DPSO) [48]. A modified DPSO solves a PDP considering DG and cross-connections [55,66]. A PDP considering DG and
storage is solved by a modified PSO with local search [71]. An evolutionary PSO solves a PDP under uncertainty considering DG [68,69].
3.2.4. Evolutionary algorithms
A decomposition based multiobjective evolutionary algorithm
seeks the Pareto front (non-dominated solutions) of a multiobjective PDP that also co-optimizes electric vehicle charging system
planning [78]. A population-based evolutionary algorithm, the
seeker optimization algorithm simultaneously optimizes PDP and
automatic reclosers allocation [80].
3.2.8. Artificial immune system (AIS)
An AIS optimization method computes a set of nearly optimal
solutions, which are next evaluated by a Monte Carlo simulation that considers load uncertainty, and, finally, the solutions are
compared via a multiobjective analysis [17]. An immune system
memetic algorithm, i.e., the AIS of [17] is combined with a network
local search to solve the PDP under load uncertainty [42].
3.2.9. Artificial bee colony (ABC)
ABC computes the network reinforcements and the commitment schedule for the installed generating units [67].
3.2.10. Practical heuristic algorithms
A heuristic approach solves a value-based distribution system
reliability planning problem [10]. The PDP is solved by a constructive heuristic algorithm [25,39,59,63]. A minimum spanning tree
method solves feeder routing problem in distribution networks
including DG [76]. A heuristic method solves a PDP in order to
increase the penetration of DG [53]. A heuristic algorithm is developed to solve the PDP and a statistical approach is introduced to
support network planers identify the best design strategy for given
types of LV networks [45]. The PDP is solved by a branch-exchange
technique in combination with minimum spanning tree [41] and
DP [44,58]. The PDP is divided into the substation problem and
the feeder problem; a pseudo-combinatorial algorithm solves the
substation problem; next, the feeder problem is solved by two
consecutive approaches: the node ordering and the node ordering
directed branch exchange [14]. The geographic zone of a secondary
distribution network is divided into small zones, and the LV PDP is
solved independently in each zone combining heuristic algorithm
and clustering technique [29]. A heuristic method for dynamic PDP
is proposed based on back-propagation of the planning procedure
starting from the final year [72].
3.3. Evaluation of PDP methods
The general PDP problem is nonlinear, non-differentiable, and
combinatorial with a large number of binary, discrete and continuous variables. This section provides an evaluation of the methods
used for PDP.
3.3.1. Evaluation of numerical methods
The numerical methods have the following advantages: the
optimal solution is usually accurate and the time to compute the
optimal solution is low. On the other hand, the numerical methods
have the following disadvantages: it is difficult to manage power
system equations into an optimization model; in order to insert a
new constraint, the optimization model has to be rearranged and
new equations have to be added.
Among the available numerical methods for PDP, the most efficient is the MINLP. In comparison to discrete numerical techniques,
the continuous ones are much faster; however, they may not find
the optimal solution due to the discretization of the continuous
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
variables. The advantage of MILP is that it is fast, robust, and efficiently handles very large scale PDP problems; however, it may
introduce errors due to the linearization of the nonlinear characteristics of PDP. The dynamic programming method is not suitable
for large-scale PDP problems.
3.3.2. Evaluation of heuristic methods
Heuristic methods are easy to use and they do not require the
conversion of the power system model into an optimization programming model. Moreover, heuristic optimization methods are
usually robust and provide near-optimal solutions for complex,
large-scale PDP problems; however, there is no guarantee that they
will find a global optimum solution. Generally, they require high
computational effort; however, this is not necessarily critical in PDP
applications.
4. Contribution of the reviewed works
Table 2 describes, in a chronological order, the main contribution of the published PDP works reviewed. The parameter related
to the active distribution network concept (if any) is also noted.
The material of Sections 2–4 and Tables 1–2 provides a guide
to the reader about the approach to choose depending on the
characteristics of the problem under consideration. The following
examples are provided:
1. The method proposed in [6] is suitable for the simultaneous planning of primary and secondary distribution grids using MILP, as
indicated in Section 3.1.1 and Table 1.
2. The approaches in [27,38] can be used for the investigation of
the impacts of DG and ADN on PDP for different regulatory environments and tariff schemes, as shown in Table 2.
3. The method described in [25] is suitable for planning of ADNs
with multiple controls (active and reactive power control of DG
units, on-line network reconfiguration, demand side response,
and generation curtailment), as shown in Table 2.
4. Efficient methods for planning active distribution networks
with controlled distributed energy resources can be found in
[19,27,32,34,38,59,60,63,64,66,68,69].
5. The approaches in [78,81] can be used for the simultaneous optimization of PDP and electric vehicle charging stations planning.
6. The method of [71] can be used for the simultaneous optimization of PDP and energy storage planning.
It is clearly beyond the scope of this paper to present to what
extent and how power distribution utilities implement modern
PDP approaches. It is well known however, that the majority of
power distribution utilities still follow traditional PDP approaches
without considering ADN concepts.
5. Future research
As already shown in the previous sections, a lot of research has
been done in the area of power distribution planning in the modern
power systems era. More specifically, Table 1 indicates that twenty
different combinations of design variables and ten different types
of objective functions have been studied in PDP, which has been
applied to three types of distribution (Section 2.4), three types of
problems (Section 2.5), and two different types of planning periods
(Section 2.6). Moreover, Table 2 shows that nine different types
of ADN components have been studied in PDP. The combination of
these different types of modelling attributes creates a large number
of PDP models. In addition, Section 3 indicates that fifteen types of
optimization methods have been already proposed to solve PDP.
95
Despite this large number of models and methods, there is clearly
significant room for PDP research.
5.1. Evolution of PDP requirements
The shift that has started in the last decade towards modern
PDP is expected to significantly increase in the years to come taking
advantage of the innovations of modern power systems, under the
terms of smart grids, distributed generation, microgrids, and active
distribution networks.
1. Regulatory framework: modifications are needed to the regulatory framework so as to give the appropriate incentives to
consider the costs and benefits of DER in the context of ADNs.
More specifically, new market rules have to be implemented
to remunerate: (1) the distribution system operators for their
ADN service that allows increasing the DG revenue; and (2) the
DER owners for the deferral of the investments their DERs can
produce. The structure of tariffs is very important for the promotion of active distribution networks and their optimal planning.
The PDP solutions have to improve the network operational performance and ensure power quality by fulfilling the regulation
standards for signal conformity and service continuity, with the
minimum impacts on the environment.
2. Coordinated planning: optimal location and sizing of capacitors,
distributed generators, and distributed energy storage systems,
and optimal planning of microgrids have to be simultaneously
considered with substations and feeders’ expansion or upgrade.
It should be noted that the upgrade of equipment (substations
and feeders) is the most commonly chosen alternative in heavy
populated urban areas, where it is very difficult and costly to
find space for new substations and to obtain rights of way for
new power distribution lines.
3. Non-dispatchable DGs: the installation of non-dispatchable DGs
(e.g., wind and photovoltaics) increases rapidly in various areas
worldwide. However, existing PDP models consider only dispatchable DGs (e.g., diesel units, gas micro-turbines, and fuel
cells). Future PDP models have to consider both types of DGs, taking also into account the DG owner (utility or private investor).
4. Uncertainties: various parameters of PDP are uncertain, e.g.,
future load growth, power of plug-in electric vehicles, market
prices, future capital costs, wind power generation, and solar
power generation. Consequently, appropriate PDP models and
solution methods, e.g., stochastic optimization, risk analysis, or
robust programming algorithms, are needed to handle these
uncertainties. Given the uncertainty in long-term PDP, the distribution networks have to be designed as flexible as possible
and DG is an alternative that offers enough flexibility.
5. Cost of reliability: successful PDP models have to quantify and
take into account the cost of reliability. The service reliability has
to include not only the service continuity but also the service
quality. Multiobjective formulations, including as objective the
reliability cost are possible. However, accurate quantification of
the reliability cost is not easy, since it requires more accurate
data both from the supplier and the customer sides.
6. Utility applications: advanced models and methods already exist
for PDP. However, the majority of distribution utilities still use
heuristic processes and empirical rules through expert judgement and practical analysis for PDP. The collaboration between
researchers and utility planners provides great opportunities for
the development of models and methods well fitted to the utility
needs and applied for real-world PDP problems of distribution
utilities.
7. New loads and storage: new components, such as heat pumps
and energy storage systems, including plug in and hybrid plug
in electric vehicles, have to be further studied in the context
96
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
Table 2
Contribution of the reviewed power distribution planning works.
Reference
Published
Contribution
[5]
Jan. 2005
[6]
May 2005
[7]
May 2005
[8]
Nov. 2005
[9]
Nov. 2005
[10]
Nov. 2005
[11]
Feb. 2006
[12]
Apr. 2006
[13]
Nov. 2006
[14]
[15]
Apr. 2007
May 2007
[16]
May 2007
[17]
May 2007
[18]
May 2007
[19]
May 2007
[20]
Apr. 2008
[21]
Apr. 2008
[22]
May 2008
[23]
May 2008
[24]
Jun. 2008
[25]
Jul. 2008
[26]
Feb. 2009
[27]
Mar. 2009
[28]
May 2009
[29]
May 2009
[30]
May 2009
[31]
May 2009
[32]
Jun. 2009
[33]
Aug. 2009
[34]
Dec. 2009
A PDP model that considers the unbalanced loads and the optimal balancing of loads to the
three phases.
An optimization model is formulated for the simultaneous planning of primary and
secondary distribution grids. The method is applied to a real case of a residential
primary–secondary distribution grid with 75 buses.
A general mathematical model is developed for the planning of low voltage power
distribution networks.
The role of individual quality of service standards in PDP and corresponding quality is
investigated. Results show how system optimal reliability and optimal quality change
with the setting of individual quality standards.
The PDP is solved by a hybrid algorithm that combines a quasi-Newton and a GA in a
sequential iteration.
A value-based probabilistic approach is developed for the design of urban power
distribution networks. The method is applied to a real urban distribution network and
practical network design rules are derived.
A fuzzy PDP model that simultaneously optimizes the economic cost, the reliability, and
the risk of overloading. Results from the application of the method in real distribution
networks show its practical usefulness.
A GA with specific crossover and mutation operators specially-designed for PDP. The
results in the form of Pareto optimal set are valuable to aid distribution companies to
decide on the investment policy.
NSGA and SPEA with a fuzzy c-means clustering algorithm solve a multiobjective PDP. The
results indicate the flexibility and the practical application of the proposed method.
Hybrid algorithms decouple the PDP into the substation and feeder sub-problems.
A PDP model that considers the reinforcement of feeders and substations as well as the
integration of DG. The results show that it is better to plan together network
reinforcement and DG instead of planning them separately.
A generalized horizon planning (20+ years ahead) for the simultaneous design of primary
and secondary grids.
The PDP under load uncertainty is solved by AIS in conjunction with Monte Carlo
simulation. Results indicate that the proposed approach provides robust network designs
under load evolution uncertainties.
The planning model [16] is validated and applied for evaluating spatial forecast impacts on
distribution design.
A novel multi-year optimization algorithm for planning active distribution networks with
DER. Real world examples illustrate the effectiveness of the proposed methodology for
planning active distribution networks.
A MILP PDP model is developed using dc power flow in combination with a linear
disjunctive model.
Evaluation of the model [20], investigating the impact of DG, investment constraints, and
load levels. A significant cost reduction is obtained when using dynamic (multistage)
planning instead of static (sequential) planning.
A SA method solves the PDP, using as initial solution the one found by a steepest descent
technique.
A multistage PDP is solved by dynamic programming GA with problem-specific fix,
crossover and mutation operators. Results show that the proposed method works for
problem sizes that exact DP is infeasible.
A multistage multiobjective PDP model for distribution substation sitting, sizing, and
timing.
A novel PDP for ADN with multiple controls including active and reactive power control of
DG units, on-line network reconfiguration, demand side response, and generation
curtailment.
A multiobjective PDP model for open-loop MV networks using geographic information
systems.
A flexible PDP evaluates different regulatory environments and tariff schemes for DER
integration. Results indicate the importance of tariff schemes in conjunction with optimal
planning of DER and network reinforcement.
Heuristic algorithms for locating HV substations, MV substations, and MV feeders. Results
indicate the ability of the proposed method for application in large-scale power
distribution planning problems.
The PDP is solved independently in each zone of the planning area considering street
constraints. The method is applied for planning a large-scale low voltage distribution
network over an area of 12.9 km2 with 20 215 consumers.
The method of [29] in combination with Voronoi diagrams and TS solves the PDP of a
distribution utility. The method is applied for planning a low voltage network over an area
of 2118 km2 with nearly 1 300 000 consumers.
A planning model that evaluates the remuneration of the fixed costs of distribution
networks with DG. Results show that simultaneous planning of DG integration and
network reinforcement can reduce reinforcement costs.
Investigation of the impact of energy carrier systems on PDP and the adequacy of system
under contingencies.
An integrated model for the simultaneous planning and development of secondary
distribution projects.
A hierarchical dynamic optimization model for PDP considering interties and investor DG
investments. Results show that capital investments in DG are barely justified by their
energy cost savings over a 10-year planning period.
ADN component
Autom. switch.
DG integration
DG integration
DG integration
DER control
Load control
DG integration
ADN with multiple controls
DER control
Load control
DER control
DER control
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
97
Table 2 (Continued)
Reference
Published
Contribution
ADN component
[35]
Mar. 2010
DG integration
[36]
Apr. 2010
[37]
Jul. 2010
[38]
Jul. 2010
[39]
Aug. 2010
[40]
Oct. 2010
[41]
Feb. 2011
[42]
Feb. 2011
[43]
[44]
May 2011
Jul. 2011
[45]
Jul. 2011
[46]
Oct. 2011
[47]
Oct. 2011
[48]
Oct. 2011
[49]
Nov. 2011
[50]
Jan. 2012
[51]
Jan. 2012
[52]
Feb. 2012
[53]
Feb. 2012
[54]
Mar. 2012
[55]
Apr. 2012
[56]
Jun. 2012
[57]
Jul. 2012
[58]
Jul. 2012
[59]
Aug. 2012
[60]
Sep. 2012
[61]
Oct. 2012
[62]
Nov. 2012
[63]
Dec. 2012
[64]
Feb. 2013
[65]
Mar. 2013
A PDP with DG connection as planning alternative, considering specific constraints related
to DG connection.
SA and TS are compared in solving nine PDP problems within 500–30 000 load points and
20 substations. Results show that the efficiency of SA decreases as the problem size
increases, and TS is more efficient than SA.
The PDP is separated by feeder areas based on an equitable distribution of loads among the
feeder areas.
The impacts of DG and ADN on PDP have been analyzed for six different regulatory
environments. The obtained results can help regulators define a fairer asset and
performance based distribution revenue.
The PDP is formulated as a mixed binary NLP problem and solved by a constructive
heuristic algorithm.
A graph theory formulation decomposes a dynamic PDP into a number of static PDP
problems. Simulation results indicate the capability of the proposed method to improve
the quality of the multistage PDP process.
Simultaneous plan for high, medium, and low voltage networks, considering the street
map for cables layout. Simulation results indicate that the incorporation of street maps
significantly affects the solution of PDP.
An immune system memetic algorithm solves more efficiently the PDP in comparison
with the AIS of [17].
A balanced GA provides higher intensity searching and filtering of the PDP solutions.
A special algorithm and the utilization of parallel computing allow the solution of
large-scale PDP problems. Results show that the proposed method efficiently optimizes
large distribution grids with thousands of loads.
A statistical approach supports decision makers identify the best design strategy for LV
distribution networks. Application results highlight the main features and the differences
in the optimal planning of urban and rural areas.
A PDP model finds a pool of solutions, assisting the decision maker to evaluate and select
from that pool. Application results help compare the reliability cost for the electric utility
and its customers.
DG integrated multistage PDP considering DG operating strategy, reliability improvement,
and load variation. Results show that the integration of DG in PDP can reduce cost and
increase reliability.
Integrated planning of MV and LV grids applicable to consumption areas with uniform and
non-uniform loads.
Planning DG integration in combination with distribution network expansion considering
DG and demand response uncertainties. Results show that better solutions are obtained
when all scenarios are analyzed simultaneously.
The optimal feeder routing is solved by a problem-specific BF technique requiring fewer
parameters to be tuned. Results show that there is a good probability the solution, which
is computed quickly, to be the global optimum.
A direct solution method to optimal feeder routing problem of radial distribution systems.
Results indicate that the proposed method reduces problem complexity without
compromising solution optimality.
Methodology for the spatial PDP considering variant environmental factors in the feeder
routing formulation. Results show that more economical planning solution can be
obtained by considering variant environmental factors.
A method to optimize current French urban network architecture (secured feeder) to
increase DG penetration.
The PDP is solved together with the placement of sectionalizing switches to reduce
non-supplied energy costs.
An integrated PDP including DG and cross-connections is proposed to improve reliability
and voltage profile. The results show that the lowest cost plan is obtained when all
technologies are simultaneously optimized.
A PDP model is proposed to determine the trade-off between minimum cost and higher
reliability.
A dynamic PDP model considering DG and the electricity market impact via a
load-dependent electricity price.
The PDP model [44] is validated and applied for solving large-scale PDP problems in
reduced time.
Investigation of the influence of the reliability of information and communication
technology on ADN planning. Preliminary results show that WiMAX communication
technology is reliable enough for application to ADNs.
A PDP considering the impact of wholesale and retail markets and the system adequacy
under contingencies.
A PDP model simultaneously optimizes the quantity, location and size of MV/LV
distribution transformers (DTs). Results show that the influence area of DT depends on
network layout, loads, and size of the DT.
Long term PDP considering urbanity uncertainties introducing the points with high
accessibility.
A PDP evaluates the impact of MV connected microgrids on grid topology, reliability, and
expansion savings. Results show that the microgrids offer considerable cost savings in
networks designed with optimal backup.
A PDP model considering DGs and upgrade of network from normally closed loop to a
mesh arrangement.
Optimal feeder routes and branch conductor sizes obtained via simultaneous optimization
of cost and reliability.
DER control
DG integration
Load control
DG integration
DG integration + demand response
Autom. switch.
Autom. switch.
DG integration
DG integration
DER control
DER control
DER control
DER control
98
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
Table 2 (Continued)
Reference
Published
Contribution
ADN component
[66]
May 2013
DER control
[67]
Jul. 2013
[68]
Aug. 2013
[69]
Aug. 2013
[70]
Oct. 2013
[71]
Nov. 2013
[72]
Dec. 2013
[73]
Dec. 2013
[74]
Jan. 2014
[75]
Mar. 2014
[76]
May 2014
[77]
May 2014
[78]
Jul. 2014
[79]
Jul. 2014
[80]
Dec. 2014
[81]
Dec. 2014
Integrated planning of DGs, capacitors, substations, and feeders using DPSO and
time-segmentation. Results demonstrate that the main benefit of dispatchable DGs is to
defer distribution network upgrade.
ABC solves dynamic PDP considering DG integration and demand variation. The proposed
ABC is applied to systems with up to 45 buses and the results are compared with those
obtained by comprehensive learning PSO.
Implementation of real options valuation to quantify the investment deferral benefit of DG
in the context of PDP.
The PDP model [68] is applied for the evaluation of DGs as expansion options to defer
network reinforcements.
PDP model for unbalanced LV distribution networks considering the impacts of micro DG
and system reliability. Results highlight the impact of unbalanced loads on the optimal
planning of low voltage distribution networks.
Integrated planning of DGs, storage units, substations, and main and reserve feeders using
modified PSO. Results show that the proposed integrated planning can reduce system cost
and increase network reliability.
A back-propagation approach based on cost–benefit analysis solves the PDP considering
DG integration.
A multiobjective multi-year PDP simultaneously considering DG allocation and network
reconfiguration. The results indicate the effectiveness of the proposed method in reducing
significantly the costs and the gas emissions.
A dynamic multistage PDP allows a comprehensive analysis of the investments made in
the planning horizon. Results demonstrate that some investments can be avoided and
others can be postponed, thus reducing the total cost.
A hybrid SA and MILP approach for expansion planning of radial distribution networks
with DG units. Results indicate that failures at DGs may have considerable impact on the
optimal expansion plan.
A graph theoretic approach including reliability assessment is proposed for feeder routing
in distribution networks with DG. The proposed approach is compared with five other
methods in power systems with up to 123 buses.
Results from joint planning of network reinforcement, renewable DG and demand
response indicate increased environmental benefits (CO2 reduction) than integrating
renewable DG alone.
Results show that the simultaneous power distribution planning and electric vehicles
charging system planning can significantly improve investment efficiency.
PDP considering the uncertainties of renewable DG output, load evolution, and electricity
price growth.
Simultaneous co-optimization of PDP and automatic reclosers allocation by seeker
optimization algorithm.
Results from the simultaneous planning of PDP and electric vehicle charging stations show
that the vehicle-to-grid features can efficiently reduce the operational costs of the power
distribution network.
of modern PDP. Energy storage units can offer peak shaving,
reliability enhancement, and increased DG penetration. The
simultaneous power distribution planning and electric vehicle
charging system planning can reduce distribution system investment and operation cost, promote the use of electric vehicles,
and reduce CO2 emissions.
8. Planning of intelligent distribution management system (IDMS):
the distribution systems of the future will face a huge penetration of distributed energy resources (DERs). IDMS with advanced
metering infrastructure will allow real-time communication
between utilities, service providers and customers to exchange
useful price and energy information together with offer and command signals. The role of IDMS is to support the integration of
DERs into distribution systems and improve the efficiency of
DERs operation [83]. The impact of IDMS on modern PDP has
to be studied.
DG integration + load control
DER control
DER control
DG integration
DG + storage
DG integration
DG integration
Autom. switch.
DG integration
DG integration
DG integration + demand response
Electric vehicles integration
DG integration
Autom. switch.
Electric vehicles integration
2. Decomposition: the PDP is a large-scale problem, because of
the size of a typical distribution network and due to the fact
that the best way to plan the system is through the multistage
(dynamic) approach. To solve the large-scale PDP, decomposition methods are applied to the size of the network (spatial
decomposition) or to the planning period (time decomposition).
As the PDP becomes even more challenging nowadays, more efficient decomposition methods for the solution of PDP are needed.
3. Initial population in heuristic algorithms: the initial population,
which is necessary in some heuristic algorithms, could be intelligently produced based on practical rules extracted from the
experience of engineers from the planning division of electric
utilities.
4. Parameters setting in heuristic methods: the optimal settings of
the parameters of the heuristic methods (e.g., GA, PSO, ACS) are
estimated in a trial and error fashion. It is proposed that these
parameters are adaptively and automatically tuned to improve
the efficiency of the heuristic PDP techniques.
5.2. Evolution of PDP methods
6. Conclusions
1. Advanced optimization methods: the PDP problem belongs to
the class of facility location and network topology optimization (FLNTO) problem. Both problems involve continuous and
discrete variables and share common characteristics. Since the
FLNTO problem forms an active research area of optimization
methods, the findings of FLNTO could be also useful for the PDP
problem.
This paper presents a thorough overview of the state of the
art models and optimization methods applied to the PDP problem in the last decade, analyzing and classifying current and future
research trends in this field. The most common PDP model of
the last decade has the following characteristics: (1) it is applied
for the static expansion of primary distribution system; (2) the
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
design variables include the integrated optimization of the location and size of substations and feeders; and (3) the objective is
the minimization of the total fixed and variable costs. It should
be noted that: (1) 55% of the reviewed PDP papers cover at least
one attribute of the active distribution network functionality, e.g.,
DER control, load control, automatic switching, and DG integration;
(2) the simultaneous optimization of the location and size of substations, DGs and feeders holds the second position among all the
design variables; and (3) the multiobjective formulation is in the
third position among all different objective functions. Moreover,
the majority of the papers published in the last two years deal with
modern PDP issues. The above findings show the shift of modern
PDP towards more integrated, multiobjective, and DG integrated
solutions with control functionalities, in comparison to the traditional PDP models. The solution methodologies for the PDP problem
are classified into two major categories: numerical and heuristic
methods. The most frequently used techniques for the solution
of the PDP problem are the genetic algorithm and various practical heuristic algorithms. Future research areas include evolution
of PDP, planning of intelligent distribution management system,
utility applications, coordinated planning, consideration of uncertainties, decomposition, and advanced optimization methods.
Acknowledgements
This work has been performed within the European Commission (EC) (308755) funded SuSTAINABLE project (contract number
FP7-ENERGY-2012.7.1.1-308755). The authors wish to thank the
SuSTAINABLE partners for their contributions and the EC for funding this project.
References
[1] P.S. Georgilakis, N.D. Hatziargyriou, Optimal distributed generation placement
in power distribution networks: models, methods, and future research, IEEE
Trans. Power Syst. 28 (3) (2013) 3420–3428.
[2] S.K. Khator, L.C. Leung, Power distribution planning: a review of models and
issues, IEEE Trans. Power Syst. 12 (3) (1997) 1151–1159.
[3] M. Vaziri, K. Tomsovic, T. Gönen, Distribution expansion problem revisited, part
1: categorical analysis and future directions, Proc. Int. Assoc. Sci. Technol. Dev.
(2000) 283–290.
[4] R. Sempértegui, J. Bautista, R.G. Cubero, J. Pereira, Models and procedures
for electric energy distribution planning. A review, in: Proc. 15th IFAC World
Congress, 2002.
[5] A.M. Cossi, R. Romero, J.R.S. Mantovani, Planning of secondary distribution circuits through evolutionary algorithms, IEEE Trans. Power Deliv. 20 (1) (2005)
205–213.
[6] P.C. Paiva, H.M. Khodr, J.A. Domínguez-Navarro, J.M. Yusta, A.J. Urdaneta, Integral planning of primary–secondary distribution systems using mixed integer
linear programming, IEEE Trans. Power Syst. 20 (2) (2005) 1134–1143.
[7] B. Türkay, T. Artac, Optimal distribution network design using genetic algorithms, Electr. Power Compon. Syst. 33 (5) (2005) 513–524.
[8] P.M.S. Carvalho, L.A.F.M. Ferreira, Distribution quality of service and reliability
optimal design: individual standards and regulation effectiveness, IEEE Trans.
Power Syst. 20 (4) (2005) 2086–2092.
[9] E.G. Carrano, R.H.C. Takahashi, E.P. Cardoso, R.R. Saldanha, O.M. Neto, Optimal
substation location and energy distribution network design using a hybrid GABFGS algorithm, IEE Proc. Gener. Transm. Distrib. 152 (6) (2005) 919–926.
[10] A.A. Chowdhury, D.E. Custer, A value-based probabilistic approach to designing urban distribution systems, Int. J. Electr. Power Energy Syst. 27 (9) (2005)
647–655.
[11] I.J. Ramírez-Rosado, J.A. Domínguez-Navarro, New multiobjective Tabu search
algorithm for fuzzy optimal planning of power distribution systems, IEEE Trans.
Power Syst. 21 (1) (2006) 224–233.
[12] E.G. Carrano, L.A.E. Soares, R.H.C. Takahashi, R.R. Saldanha, O.M. Neto, Electric
distribution network multiobjective design using a problem-specific genetic
algorithm, IEEE Trans. Power Deliv. 21 (2) (2006) 995–1005.
[13] F. Mendoza, J.L. Bernal-Agustín, J.A. Domínguez-Navarro, NSGA and SPEA
applied to multiobjective design of power distribution systems, IEEE Trans.
Power Syst. 21 (4) (2006) 1938–1945.
[14] H. Zhao, Z. Wang, D.C. Yu, X. Chen, New formulations and hybrid algorithms
for distribution system planning, Electr. Power Compon. Syst. 35 (4) (2007)
445–460.
[15] S. Favuzza, G. Graditi, M.G. Ippolito, E.R. Sanseverino, Optimal electrical distribution systems reinforcement planning using gas micro turbines by dynamic
ant colony search algorithm, IEEE Trans. Power Syst. 22 (2) (2007) 580–587.
99
[16] R.H. Fletcher, K. Strunz, Optimal distribution system horizon planning – part I:
formulation, IEEE Trans. Power Syst. 22 (2) (2007) 791–799.
[17] E.G. Carrano, F.G. Guimarães, R.H.C. Takahashi, O.M. Neto, F. Campelo, Electric distribution network expansion under load-evolution uncertainty using
an immune system inspired algorithm, IEEE Trans. Power Syst. 22 (2) (2007)
851–861.
[18] R.H. Fletcher, K. Strunz, Optimal distribution system horizon planning – part
II: application, IEEE Trans. Power Syst. 22 (2) (2007) 862–870.
[19] G. Celli, S. Mocci, F. Pilo, D. Bertini, R. Cicoria, S. Corti, Multi-year optimal planning of active distribution networks, in: Proc. CIRED, 2007.
[20] S. Haffner, L.F.A. Pereira, L.A. Pereira, L.S. Barreto, Multistage model for distribution expansion planning with distributed generation – part I: problem
formulation, IEEE Trans. Power Deliv. 23 (2) (2008) 915–923.
[21] S. Haffner, L.F.A. Pereira, L.A. Pereira, L.S. Barreto, Multistage model for distribution expansion planning with distributed generation – part II: numerical
results, IEEE Trans. Power Deliv. 23 (2) (2008) 924–929.
[22] J.M. Nahman, D.M. Perić, Optimal planning of radial distribution networks by
simulated annealing technique, IEEE Trans. Power Syst. 23 (2) (2008) 790–795.
[23] E.G. Carrano, R.T.N. Cardoso, R.H.C. Takahashi, C.M. Fonseca, O.M. Neto,
Power distribution network expansion scheduling using dynamic programming genetic algorithm, IET Gener. Transm. Distrib. 2 (3) (2008) 444–455.
[24] T.H.M. El-Fouly, H.H. Zeineldin, E.F. El-Saadany, M.M.A. Salama, A new optimization model for distribution substation sitting, sizing, and timing, Int. J.
Electr. Power Energy Syst. 30 (5) (2008) 308–315.
[25] G. Celli, F. Pilo, G. Pisano, G.G. Soma, Optimal planning of active networks, in:
Proc. PSCC, 2008.
[26] T. Kong, H. Cheng, Z. Hu, L. Yao, Multiobjective planning of open-loop MV distribution networks using ComGIS network analysis and MOGA, Electr. Power
Syst. Res. 79 (2) (2009) 390–398.
[27] E. Haesen, A.D. Alarcon-Rodriguez, J. Driesen, R. Belmans, G. Ault, Opportunities
for active DER management in deferral of distribution system reinforcements,
in: Proc. PSCE, 2009.
[28] S. Najafi, S.H. Hosseinian, M. Abedi, A. Vahidnia, S. Abachezadeh, A framework
for optimal planning in large distribution networks, IEEE Trans. Power Syst. 24
(2) (2009) 1019–1028.
[29] A. Navarro, H. Rudnick, Large-scale distribution planning – part I: simultaneous
network and transformer optimization, IEEE Trans. Power Syst. 24 (2) (2009)
744–751.
[30] A. Navarro, H. Rudnick, Large-scale distribution planning – part II: macrooptimization with Voronoi’s diagram and Tabu search, IEEE Trans. Power Syst.
24 (2) (2009) 752–758.
[31] H.M. Khodr, Z.A. Vale, C. Ramos, A Benders decomposition and fuzzy multicriteria approach for distribution networks remuneration considering DG, IEEE
Trans. Power Syst. 24 (2) (2009) 1091–1101.
[32] M.S. Nazar, M.R. Haghifam, Multiobjective electric distribution system expansion planning using hybrid energy hub concept, Electr. Power Syst. Res. 79 (6)
(2009) 899–911.
[33] A.M. Cossi, R. Romero, J.R.S. Mantovani, Planning and projects of secondary
electric power distribution systems, IEEE Trans. Power Syst. 24 (3) (2009)
1599–1608.
[34] S. Wong, K. Bhattacharya, J.D. Fuller, Electric power distribution system design
and planning in a deregulated environment, IET Gener. Transm. Distrib. 3 (12)
(2009) 1061–1078.
[35] W. Ouyang, H. Cheng, X. Zhang, L. Yao, M. Bazargan, Distribution network planning considering distributed generation by genetic algorithm combined with
graph theory, Electr. Power Compon. Syst. 38 (3) (2010) 325–339.
[36] V. Parada, J.A. Ferland, M. Arias, P. Schwarzenberg, L.S. Vargas, Heuristic determination of distribution trees, IEEE Trans. Power Deliv. 25 (2) (2010) 861–869.
[37] G.A. Jiménez-Estévez, L.S. Vargas, V. Marianov, Determination of feeder areas
for the design of large distribution networks, IEEE Trans. Power Deliv. 25 (3)
(2010) 1912–1922.
[38] F. Pilo, G. Celli, S. Mocci, G.G. Soma, Multi-objective programming for optimal
DG integration in active distribution systems, in: Proc. IEEE PES GM, 2010.
[39] M. Lavorato, M.J. Rider, A.V. Garcia, R. Romero, A constructive heuristic algorithm for distribution system planning, IEEE Trans. Power Syst. 25 (3) (2010)
1734–1742.
[40] Ž.N. Popović, D.S. Popović, Graph theory based formulation of multi-period
distribution expansion problems, Electr. Power Syst. Res. 80 (10) (2010)
1256–1266.
[41] C.M. Domingo, T.G.S. Román, Á. Sánchez-Miralles, J.P.P. González, A.C. Martínez,
A reference network model for large-scale distribution planning with automatic street map generation, IEEE Trans. Power Syst. 26 (1) (2011) 190–197.
[42] B.B. Souza, E.G. Carrano, O.M. Neto, R.H.C. Takahashi, Immune system memetic
algorithm for power distribution network design with load evolution uncertainty, Electr. Power Syst. Res. 81 (2) (2011) 527–537.
[43] D.T.C. Wang, L.F. Ochoa, G.P. Harrison, Modified GA and data envelopment analysis for multistage distribution network expansion planning under uncertainty,
IEEE Trans. Power Syst. 26 (2) (2011) 897–904.
[44] J.C. Moreira, E. Míguez, C. Vilachá, A.F. Otero, Large-scale network layout optimization for radial distribution networks by parallel computing, IEEE Trans.
Power Deliv. 26 (3) (2011) 1946–1951.
[45] C.K. Gan, P. Mancarella, D. Pudjianto, G. Strbac, Statistical appraisal of economic
design strategies of LV distribution networks, Electr. Power Syst. Res. 81 (7)
(2011) 1363–1372.
[46] R.C. Lotero, J. Contreras, Distribution system planning with reliability, IEEE
Trans. Power Deliv. 26 (4) (2011) 2552–2562.
100
P.S. Georgilakis, N.D. Hatziargyriou / Electric Power Systems Research 121 (2015) 89–100
[47] H. Falaghi, C. Singh, M.R. Haghifam, M. Ramezani, DG integrated multistage
distribution system expansion planning, Int. J. Electr. Power Energy Syst. 33 (8)
(2011) 1489–1497.
[48] I. Ziari, G. Ledwich, A. Ghosh, Optimal integrated planning of MV-LV distribution
systems using DPSO, Electr. Power Syst. Res. 81 (10) (2011) 1905–1914.
[49] V.F. Martins, C.L.T. Borges, Active distribution network integrated planning
incorporating distributed generation and load response uncertainties, IEEE
Trans. Power Syst. 26 (4) (2011) 2164–2172.
[50] S. Singh, T. Ghose, S.K. Goswami, Optimal feeder routing based on the bacterial
foraging technique, IEEE Trans. Power Deliv. 27 (1) (2012) 70–78.
[51] A. Samui, S. Singh, T. Ghose, S.R. Samantaray, A direct approach to optimal
feeder routing for radial distribution system, IEEE Trans. Power Deliv. 27 (1)
(2012) 253–260.
[52] J. Shu, L. Wu, Z. Li, M. Shahidehpour, L. Zhang, B. Han, A new method for spatial
power network planning in complicated environments, IEEE Trans. Power Syst.
27 (1) (2012) 381–389.
[53] M.C. Alvarez-Herault, R. Caire, B. Raison, N. HadjSaid, W. Biena, Optimizing
traditional urban network architectures to increase distributed generation connection, Int. J. Electr. Power Energy Syst. 35 (1) (2012) 148–157.
[54] A.M. Cossi, L.G.W. Da Silva, R.A.R. Lázaro, J.R.S. Mantovani, Primary power
distribution systems planning taking into account reliability, operation and
expansion costs, IET Gener. Transm. Distrib. 6 (3) (2012) 274–284.
[55] I. Ziari, G. Ledwich, A. Ghosh, G. Platt, Integrated distribution systems planning
to improve reliability under load growth, IEEE Trans. Power Deliv. 27 (2) (2012)
757–765.
[56] A. Samui, S.R. Samantaray, G. Panda, Distribution system planning considering
reliable feeder routing, IET Gener. Transm. Distrib. 6 (6) (2012) 503–514.
[57] E. Naderi, H. Seifi, M.S. Sepasian, A dynamic approach for distribution system
planning considering distributed generation, IEEE Trans. Power Deliv. 27 (3)
(2012) 1313–1322.
[58] J.C. Moreira, E. Míguez, C. Vilachá, A.F. Otero, Large-scale network layout
optimization for radial distribution networks by parallel computing: implementation and numerical results, IEEE Trans. Power Deliv. 27 (3) (2012)
1468–1476.
[59] G. Celli, E. Ghiani, G.G. Soma, F. Pilo, Planning of reliable active distribution
systems, in: Proc. CIGRE, 2012.
[60] M.S. Nazar, M.R. Haghifam, M. Nažar, A scenario driven multiobjective
primary–secondary distribution system expansion planning algorithm in the
presence of wholesale–retail market, Int. J. Electr. Power Energy Syst. 40 (1)
(2012) 29–45.
[61] J.E. Mendoza, M.E. López, H.E. Pena, D.A. Labra, Low voltage distribution optimization: site, quantity and size of distribution transformers, Electr. Power
Syst. Res. 91 (2012) 52–60.
[62] J. Salehi, M.R. Haghifam, Long term distribution network planning considering
urbanity uncertainties, Int. J. Electr. Power Energy Syst. 42 (1) (2012) 321–333.
[63] R.J. Millar, S. Kazemi, M. Lehtonen, E. Saarijärvi, Impact of MV connected
microgrids on MV distribution planning, IEEE Trans. Smart Grid 3 (4) (2012)
2100–2108.
[64] T.H. Chen, E.H. Lin, N.C. Yang, T.Y. Hsieh, Multi-objective optimization for
upgrading primary feeders with distributed generators from normally closed
loop to mesh arrangement, Int. J. Electr. Power Energy Syst. 45 (1) (2013)
413–419.
[65] S. Ganguly, N.C. Sahoo, D. Das, Multi-objective planning of electrical distribution systems using dynamic programming, Int. J. Electr. Power Energy Syst. 46
(2013) 65–78.
[66] I. Ziari, G. Ledwich, A. Ghosh, G. Platt, Optimal distribution network reinforcement considering load growth, line loss, and reliability, IEEE Trans. Power Syst.
28 (2) (2013) 587–597.
[67] A.M. El-Zonkoly, Multistage expansion planning for distribution networks
including unit commitment, IET Gener. Transm. Distrib. 7 (7) (2013) 766–778.
[68] M.E. Samper, A. Vargas, Investment decisions in distribution networks under
uncertainty with distributed generation – part I: model formulation, IEEE Trans.
Power Syst. 28 (3) (2013) 2331–2340.
[69] M.E. Samper, A. Vargas, Investment decisions in distribution networks under
uncertainty with distributed generation – part II: implementation and results,
IEEE Trans. Power Syst. 28 (3) (2013) 2341–2351.
[70] J.E. Mendoza, M.E. López, S.C. Fingerhuth, H.E. Pena, C.A. Salinas, Low voltage
distribution planning considering micro distributed generation, Electr. Power
Syst. Res. 103 (2013) 233–240.
[71] M. Sedghi, M. Aliakbar-Golkar, M.R. Haghifam, Distribution network expansion considering distributed generation and storage units using modified PSO
algorithm, Int. J. Electr. Power Energy Syst. 52 (2013) 221–230.
[72] A.S.B. Humayd, K. Bhattacharya, Comprehensive multi-year distribution system planning using back-propagation approach, IET Gener. Transm. Distrib. 7
(12) (2013) 1415–1425.
[73] A. Zidan, M.F. Shaaban, E.E. El-Saadany, Long-term multi-objective distribution
network planning by DG allocation and feeders’ reconfiguration, Electr. Power
Syst. Res. 105 (2013) 95–104.
[74] B.R. Pereira Junior, A.M. Cossi, J. Contreras, J.R.S. Mantovani, Multiobjective
multistage distribution system planning using Tabu search, IET Gener. Transm.
Distrib. 8 (1) (2014) 35–45.
[75] Ž.N. Popović, V.D. Kerleta, D.S. Popović, Hybrid simulated annealing and mixed
integer linear programming algorithm for optimal planning of radial distribution networks with distributed generation, Electr. Power Syst. Res. 108 (2014)
211–222.
[76] D. Kumar, S.R. Samantaray, G. Joos, A reliability assessment based graph
theoretical approach for feeder routing in power distribution networks including distributed generations, Int. J. Electr. Power Energy Syst. 57 (2014)
11–30.
[77] B. Zeng, J. Zhang, X. Yang, J. Wang, J. Dong, Y. Zhang, Integrated planning for transition to low-carbon distribution system with renewable energy generation
and demand response, IEEE Trans. Power Syst. 29 (3) (2014) 1153–1165.
[78] W. Yao, J. Zhao, F. Wen, Z. Dong, Y. Xue, Y. Xu, K. Meng, A multi-objective
collaborative planning strategy for integrated power distribution and electric vehicle charging systems, IEEE Trans. Power Syst. 29 (4) (2014) 1811–
1821.
[79] N.C. Koutsoukis, P.S. Georgilakis, N.D. Hatziargyriou, A Tabu search method for
distribution network planning considering distributed generation and uncertainties, in: Proc. PMAPS, 2014.
[80] D. Kumar, S.R. Samantaray, Design of an advanced electric power distribution
systems using seeker optimization algorithm, Int. J. Electr. Power Energy Syst.
63 (2014) 196–217.
[81] X. Lin, J. Sun, S. Ai, X. Xiong, Y. Wan, D. Yang, Distribution network planning
integrating charging stations of electric vehicle with V2G, Int. J. Electr. Power
Energy Syst. 63 (2014) 507–512.
[82] R.T. Marler, J.S. Arora, Survey of multi-objective optimization methods for engineering, Struct. Multidiscip. Optim. 26 (2004) 369–395.
[83] A. Zakariazadeh, S. Jadid, P. Siano, Stochastic multi-objective operational planning of smart distribution systems considering demand response programs,
Electr. Power Syst. Res. 111 (2014) 156–168.